LMFDB - Embedded newform 8030.2.a.bd.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8030,2,Mod(1,8030)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8030, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8030 = 2 \cdot 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8030.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.1198728231$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 6 x^{13} - 15 x^{12} + 143 x^{11} - 13 x^{10} - 1176 x^{9} + 1018 x^{8} + 4076 x^{7} + \cdots - 54 $ x^14 - 6x^13 - 15x^12 + 143x^11 - 13x^10 - 1176x^9 + 1018x^8 + 4076x^7 - 4865x^6 - 5483x^5 + 7607x^4 + 1210x^3 - 3153x^2 + 878*x - 54
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.331408$ of defining polynomial
Character	$\chi$	$=$	8030.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.331408 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.331408 q^{6} +4.90237 q^{7} +1.00000 q^{8} -2.89017 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.331408 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.331408 q^{6} +4.90237 q^{7} +1.00000 q^{8} -2.89017 q^{9} -1.00000 q^{10} +1.00000 q^{11} +0.331408 q^{12} -6.37989 q^{13} +4.90237 q^{14} -0.331408 q^{15} +1.00000 q^{16} +2.92330 q^{17} -2.89017 q^{18} -2.09641 q^{19} -1.00000 q^{20} +1.62468 q^{21} +1.00000 q^{22} -3.56759 q^{23} +0.331408 q^{24} +1.00000 q^{25} -6.37989 q^{26} -1.95205 q^{27} +4.90237 q^{28} -2.29315 q^{29} -0.331408 q^{30} +6.50101 q^{31} +1.00000 q^{32} +0.331408 q^{33} +2.92330 q^{34} -4.90237 q^{35} -2.89017 q^{36} +4.91092 q^{37} -2.09641 q^{38} -2.11434 q^{39} -1.00000 q^{40} -10.0332 q^{41} +1.62468 q^{42} +7.00187 q^{43} +1.00000 q^{44} +2.89017 q^{45} -3.56759 q^{46} +9.05617 q^{47} +0.331408 q^{48} +17.0333 q^{49} +1.00000 q^{50} +0.968804 q^{51} -6.37989 q^{52} +10.4014 q^{53} -1.95205 q^{54} -1.00000 q^{55} +4.90237 q^{56} -0.694765 q^{57} -2.29315 q^{58} +13.4141 q^{59} -0.331408 q^{60} -1.92859 q^{61} +6.50101 q^{62} -14.1687 q^{63} +1.00000 q^{64} +6.37989 q^{65} +0.331408 q^{66} +5.86942 q^{67} +2.92330 q^{68} -1.18233 q^{69} -4.90237 q^{70} +14.8467 q^{71} -2.89017 q^{72} +1.00000 q^{73} +4.91092 q^{74} +0.331408 q^{75} -2.09641 q^{76} +4.90237 q^{77} -2.11434 q^{78} -4.63200 q^{79} -1.00000 q^{80} +8.02358 q^{81} -10.0332 q^{82} +5.01023 q^{83} +1.62468 q^{84} -2.92330 q^{85} +7.00187 q^{86} -0.759967 q^{87} +1.00000 q^{88} +4.69580 q^{89} +2.89017 q^{90} -31.2766 q^{91} -3.56759 q^{92} +2.15449 q^{93} +9.05617 q^{94} +2.09641 q^{95} +0.331408 q^{96} +5.24479 q^{97} +17.0333 q^{98} -2.89017 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 14 q^{2} + 6 q^{3} + 14 q^{4} - 14 q^{5} + 6 q^{6} + 4 q^{7} + 14 q^{8} + 24 q^{9}+O(q^{10}) $ 14 * q + 14 * q^2 + 6 * q^3 + 14 * q^4 - 14 * q^5 + 6 * q^6 + 4 * q^7 + 14 * q^8 + 24 * q^9	\( 14 q + 14 q^{2} + 6 q^{3} + 14 q^{4} - 14 q^{5} + 6 q^{6} + 4 q^{7} + 14 q^{8} + 24 q^{9} - 14 q^{10} + 14 q^{11} + 6 q^{12} + 4 q^{13} + 4 q^{14} - 6 q^{15} + 14 q^{16} + 20 q^{17} + 24 q^{18} - 14 q^{20} + 25 q^{21} + 14 q^{22} - 4 q^{23} + 6 q^{24} + 14 q^{25} + 4 q^{26} + 21 q^{27} + 4 q^{28} + 7 q^{29} - 6 q^{30} + 8 q^{31} + 14 q^{32} + 6 q^{33} + 20 q^{34} - 4 q^{35} + 24 q^{36} + 17 q^{37} + 7 q^{39} - 14 q^{40} - 14 q^{41} + 25 q^{42} + 12 q^{43} + 14 q^{44} - 24 q^{45} - 4 q^{46} + 28 q^{47} + 6 q^{48} + 20 q^{49} + 14 q^{50} - 13 q^{51} + 4 q^{52} + 13 q^{53} + 21 q^{54} - 14 q^{55} + 4 q^{56} - 23 q^{57} + 7 q^{58} + 36 q^{59} - 6 q^{60} + 25 q^{61} + 8 q^{62} + 45 q^{63} + 14 q^{64} - 4 q^{65} + 6 q^{66} + 20 q^{68} - 7 q^{69} - 4 q^{70} + 17 q^{71} + 24 q^{72} + 14 q^{73} + 17 q^{74} + 6 q^{75} + 4 q^{77} + 7 q^{78} + 10 q^{79} - 14 q^{80} + 58 q^{81} - 14 q^{82} - 6 q^{83} + 25 q^{84} - 20 q^{85} + 12 q^{86} + 44 q^{87} + 14 q^{88} + 36 q^{89} - 24 q^{90} - 15 q^{91} - 4 q^{92} - 2 q^{93} + 28 q^{94} + 6 q^{96} - 19 q^{97} + 20 q^{98} + 24 q^{99}+O(q^{100}) \) 14 * q + 14 * q^2 + 6 * q^3 + 14 * q^4 - 14 * q^5 + 6 * q^6 + 4 * q^7 + 14 * q^8 + 24 * q^9 - 14 * q^10 + 14 * q^11 + 6 * q^12 + 4 * q^13 + 4 * q^14 - 6 * q^15 + 14 * q^16 + 20 * q^17 + 24 * q^18 - 14 * q^20 + 25 * q^21 + 14 * q^22 - 4 * q^23 + 6 * q^24 + 14 * q^25 + 4 * q^26 + 21 * q^27 + 4 * q^28 + 7 * q^29 - 6 * q^30 + 8 * q^31 + 14 * q^32 + 6 * q^33 + 20 * q^34 - 4 * q^35 + 24 * q^36 + 17 * q^37 + 7 * q^39 - 14 * q^40 - 14 * q^41 + 25 * q^42 + 12 * q^43 + 14 * q^44 - 24 * q^45 - 4 * q^46 + 28 * q^47 + 6 * q^48 + 20 * q^49 + 14 * q^50 - 13 * q^51 + 4 * q^52 + 13 * q^53 + 21 * q^54 - 14 * q^55 + 4 * q^56 - 23 * q^57 + 7 * q^58 + 36 * q^59 - 6 * q^60 + 25 * q^61 + 8 * q^62 + 45 * q^63 + 14 * q^64 - 4 * q^65 + 6 * q^66 + 20 * q^68 - 7 * q^69 - 4 * q^70 + 17 * q^71 + 24 * q^72 + 14 * q^73 + 17 * q^74 + 6 * q^75 + 4 * q^77 + 7 * q^78 + 10 * q^79 - 14 * q^80 + 58 * q^81 - 14 * q^82 - 6 * q^83 + 25 * q^84 - 20 * q^85 + 12 * q^86 + 44 * q^87 + 14 * q^88 + 36 * q^89 - 24 * q^90 - 15 * q^91 - 4 * q^92 - 2 * q^93 + 28 * q^94 + 6 * q^96 - 19 * q^97 + 20 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.331408	0.191338	0.0956691	−	0.995413i	$-0.469501\pi$
$3$	0.331408	0.191338	0.0956691	+	0.995413i	$0.469501\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.331408	0.135297
$7$	4.90237	1.85292	0.926461	−	0.376390i	$-0.122835\pi$
$7$	4.90237	1.85292	0.926461	+	0.376390i	$0.122835\pi$
$8$	1.00000	0.353553
$9$	−2.89017	−0.963390
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.331408	0.0956691
$13$	−6.37989	−1.76946	−0.884731	−	0.466102i	$-0.845658\pi$
$13$	−6.37989	−1.76946	−0.884731	+	0.466102i	$0.845658\pi$
$14$	4.90237	1.31021
$15$	−0.331408	−0.0855691
$16$	1.00000	0.250000
$17$	2.92330	0.709004	0.354502	−	0.935055i	$-0.384650\pi$
$17$	2.92330	0.709004	0.354502	+	0.935055i	$0.384650\pi$
$18$	−2.89017	−0.681219
$19$	−2.09641	−0.480949	−0.240474	−	0.970655i	$-0.577303\pi$
$19$	−2.09641	−0.480949	−0.240474	+	0.970655i	$0.577303\pi$
$20$	−1.00000	−0.223607
$21$	1.62468	0.354535
$22$	1.00000	0.213201
$23$	−3.56759	−0.743894	−0.371947	−	0.928254i	$-0.621310\pi$
$23$	−3.56759	−0.743894	−0.371947	+	0.928254i	$0.621310\pi$
$24$	0.331408	0.0676483
$25$	1.00000	0.200000
$26$	−6.37989	−1.25120
$27$	−1.95205	−0.375672
$28$	4.90237	0.926461
$29$	−2.29315	−0.425827	−0.212914	−	0.977071i	$-0.568295\pi$
$29$	−2.29315	−0.425827	−0.212914	+	0.977071i	$0.568295\pi$
$30$	−0.331408	−0.0605065
$31$	6.50101	1.16762	0.583808	−	0.811891i	$-0.301562\pi$
$31$	6.50101	1.16762	0.583808	+	0.811891i	$0.301562\pi$
$32$	1.00000	0.176777
$33$	0.331408	0.0576907
$34$	2.92330	0.501342
$35$	−4.90237	−0.828652
$36$	−2.89017	−0.481695
$37$	4.91092	0.807351	0.403676	−	0.914902i	$-0.367732\pi$
$37$	4.91092	0.807351	0.403676	+	0.914902i	$0.367732\pi$
$38$	−2.09641	−0.340082
$39$	−2.11434	−0.338566
$40$	−1.00000	−0.158114
$41$	−10.0332	−1.56692	−0.783458	−	0.621445i	$-0.786546\pi$
$41$	−10.0332	−1.56692	−0.783458	+	0.621445i	$0.786546\pi$
$42$	1.62468	0.250694
$43$	7.00187	1.06778	0.533888	−	0.845555i	$-0.320731\pi$
$43$	7.00187	1.06778	0.533888	+	0.845555i	$0.320731\pi$
$44$	1.00000	0.150756
$45$	2.89017	0.430841
$46$	−3.56759	−0.526012
$47$	9.05617	1.32098	0.660489	−	0.750836i	$-0.270349\pi$
$47$	9.05617	1.32098	0.660489	+	0.750836i	$0.270349\pi$
$48$	0.331408	0.0478346
$49$	17.0333	2.43332
$50$	1.00000	0.141421
$51$	0.968804	0.135660
$52$	−6.37989	−0.884731
$53$	10.4014	1.42875	0.714373	−	0.699765i	$-0.246712\pi$
$53$	10.4014	1.42875	0.714373	+	0.699765i	$0.246712\pi$
$54$	−1.95205	−0.265640
$55$	−1.00000	−0.134840
$56$	4.90237	0.655107
$57$	−0.694765	−0.0920239
$58$	−2.29315	−0.301105
$59$	13.4141	1.74636	0.873181	−	0.487396i	$-0.162053\pi$
$59$	13.4141	1.74636	0.873181	+	0.487396i	$0.162053\pi$
$60$	−0.331408	−0.0427845
$61$	−1.92859	−0.246930	−0.123465	−	0.992349i	$-0.539401\pi$
$61$	−1.92859	−0.246930	−0.123465	+	0.992349i	$0.539401\pi$
$62$	6.50101	0.825630
$63$	−14.1687	−1.78509
$64$	1.00000	0.125000
$65$	6.37989	0.791327
$66$	0.331408	0.0407935
$67$	5.86942	0.717064	0.358532	−	0.933517i	$-0.383277\pi$
$67$	5.86942	0.717064	0.358532	+	0.933517i	$0.383277\pi$
$68$	2.92330	0.354502
$69$	−1.18233	−0.142335
$70$	−4.90237	−0.585946
$71$	14.8467	1.76198	0.880991	−	0.473134i	$-0.156877\pi$
$71$	14.8467	1.76198	0.880991	+	0.473134i	$0.156877\pi$
$72$	−2.89017	−0.340610
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	4.91092	0.570883
$75$	0.331408	0.0382676
$76$	−2.09641	−0.240474
$77$	4.90237	0.558677
$78$	−2.11434	−0.239402
$79$	−4.63200	−0.521141	−0.260571	−	0.965455i	$-0.583911\pi$
$79$	−4.63200	−0.521141	−0.260571	+	0.965455i	$0.583911\pi$
$80$	−1.00000	−0.111803
$81$	8.02358	0.891509
$82$	−10.0332	−1.10798
$83$	5.01023	0.549944	0.274972	−	0.961452i	$-0.411331\pi$
$83$	5.01023	0.549944	0.274972	+	0.961452i	$0.411331\pi$
$84$	1.62468	0.177267
$85$	−2.92330	−0.317076
$86$	7.00187	0.755031
$87$	−0.759967	−0.0814770
$88$	1.00000	0.106600
$89$	4.69580	0.497754	0.248877	−	0.968535i	$-0.419938\pi$
$89$	4.69580	0.497754	0.248877	+	0.968535i	$0.419938\pi$
$90$	2.89017	0.304651
$91$	−31.2766	−3.27868
$92$	−3.56759	−0.371947
$93$	2.15449	0.223410
$94$	9.05617	0.934073
$95$	2.09641	0.215087
$96$	0.331408	0.0338241
$97$	5.24479	0.532528	0.266264	−	0.963900i	$-0.414211\pi$
$97$	5.24479	0.532528	0.266264	+	0.963900i	$0.414211\pi$
$98$	17.0333	1.72062
$99$	−2.89017	−0.290473
$100$	1.00000	0.100000
$101$	−2.40874	−0.239679	−0.119839	−	0.992793i	$-0.538238\pi$
$101$	−2.40874	−0.239679	−0.119839	+	0.992793i	$0.538238\pi$
$102$	0.968804	0.0959259
$103$	10.6983	1.05413	0.527065	−	0.849825i	$-0.323292\pi$
$103$	10.6983	1.05413	0.527065	+	0.849825i	$0.323292\pi$
$104$	−6.37989	−0.625599
$105$	−1.62468	−0.158553
$106$	10.4014	1.01028
$107$	13.6952	1.32396	0.661981	−	0.749521i	$-0.269716\pi$
$107$	13.6952	1.32396	0.661981	+	0.749521i	$0.269716\pi$
$108$	−1.95205	−0.187836
$109$	18.5167	1.77357	0.886787	−	0.462178i	$-0.152932\pi$
$109$	18.5167	1.77357	0.886787	+	0.462178i	$0.152932\pi$
$110$	−1.00000	−0.0953463
$111$	1.62752	0.154477
$112$	4.90237	0.463231
$113$	−9.01739	−0.848284	−0.424142	−	0.905596i	$-0.639424\pi$
$113$	−9.01739	−0.848284	−0.424142	+	0.905596i	$0.639424\pi$
$114$	−0.694765	−0.0650707
$115$	3.56759	0.332679
$116$	−2.29315	−0.212914
$117$	18.4389	1.70468
$118$	13.4141	1.23486
$119$	14.3311	1.31373
$120$	−0.331408	−0.0302532
$121$	1.00000	0.0909091
$122$	−1.92859	−0.174606
$123$	−3.32506	−0.299811
$124$	6.50101	0.583808
$125$	−1.00000	−0.0894427
$126$	−14.1687	−1.26225
$127$	−13.9069	−1.23404	−0.617020	−	0.786947i	$-0.711660\pi$
$127$	−13.9069	−1.23404	−0.617020	+	0.786947i	$0.711660\pi$
$128$	1.00000	0.0883883
$129$	2.32047	0.204306
$130$	6.37989	0.559553
$131$	−16.1976	−1.41519	−0.707595	−	0.706618i	$-0.750220\pi$
$131$	−16.1976	−1.41519	−0.707595	+	0.706618i	$0.750220\pi$
$132$	0.331408	0.0288453
$133$	−10.2774	−0.891161
$134$	5.86942	0.507041
$135$	1.95205	0.168005
$136$	2.92330	0.250671
$137$	−12.5110	−1.06889	−0.534445	−	0.845203i	$-0.679479\pi$
$137$	−12.5110	−1.06889	−0.534445	+	0.845203i	$0.679479\pi$
$138$	−1.18233	−0.100646
$139$	−4.10209	−0.347935	−0.173967	−	0.984751i	$-0.555659\pi$
$139$	−4.10209	−0.347935	−0.173967	+	0.984751i	$0.555659\pi$
$140$	−4.90237	−0.414326
$141$	3.00128	0.252754
$142$	14.8467	1.24591
$143$	−6.37989	−0.533513
$144$	−2.89017	−0.240847
$145$	2.29315	0.190436
$146$	1.00000	0.0827606
$147$	5.64495	0.465588
$148$	4.91092	0.403676
$149$	−11.4127	−0.934966	−0.467483	−	0.884002i	$-0.654839\pi$
$149$	−11.4127	−0.934966	−0.467483	+	0.884002i	$0.654839\pi$
$150$	0.331408	0.0270593
$151$	−21.4371	−1.74453	−0.872264	−	0.489035i	$-0.837349\pi$
$151$	−21.4371	−1.74453	−0.872264	+	0.489035i	$0.837349\pi$
$152$	−2.09641	−0.170041
$153$	−8.44883	−0.683048
$154$	4.90237	0.395044
$155$	−6.50101	−0.522174
$156$	−2.11434	−0.169283
$157$	5.76926	0.460437	0.230218	−	0.973139i	$-0.426056\pi$
$157$	5.76926	0.460437	0.230218	+	0.973139i	$0.426056\pi$
$158$	−4.63200	−0.368502
$159$	3.44711	0.273374
$160$	−1.00000	−0.0790569
$161$	−17.4896	−1.37838
$162$	8.02358	0.630392
$163$	−13.5070	−1.05795	−0.528977	−	0.848636i	$-0.677424\pi$
$163$	−13.5070	−1.05795	−0.528977	+	0.848636i	$0.677424\pi$
$164$	−10.0332	−0.783458
$165$	−0.331408	−0.0258000
$166$	5.01023	0.388869
$167$	−12.6024	−0.975205	−0.487602	−	0.873066i	$-0.662128\pi$
$167$	−12.6024	−0.975205	−0.487602	+	0.873066i	$0.662128\pi$
$168$	1.62468	0.125347
$169$	27.7029	2.13100
$170$	−2.92330	−0.224207
$171$	6.05897	0.463341
$172$	7.00187	0.533888
$173$	12.4322	0.945204	0.472602	−	0.881276i	$-0.343315\pi$
$173$	12.4322	0.945204	0.472602	+	0.881276i	$0.343315\pi$
$174$	−0.759967	−0.0576129
$175$	4.90237	0.370585
$176$	1.00000	0.0753778
$177$	4.44552	0.334146
$178$	4.69580	0.351965
$179$	26.4722	1.97863	0.989314	−	0.145800i	$-0.0465754\pi$
$179$	26.4722	1.97863	0.989314	+	0.145800i	$0.0465754\pi$
$180$	2.89017	0.215420
$181$	24.0587	1.78827	0.894136	−	0.447795i	$-0.147791\pi$
$181$	24.0587	1.78827	0.894136	+	0.447795i	$0.147791\pi$
$182$	−31.2766	−2.31837
$183$	−0.639148	−0.0472472
$184$	−3.56759	−0.263006
$185$	−4.91092	−0.361058
$186$	2.15449	0.157975
$187$	2.92330	0.213773
$188$	9.05617	0.660489
$189$	−9.56966	−0.696090
$190$	2.09641	0.152089
$191$	−13.3900	−0.968864	−0.484432	−	0.874829i	$-0.660974\pi$
$191$	−13.3900	−0.968864	−0.484432	+	0.874829i	$0.660974\pi$
$192$	0.331408	0.0239173
$193$	11.9668	0.861388	0.430694	−	0.902498i	$-0.358269\pi$
$193$	11.9668	0.861388	0.430694	+	0.902498i	$0.358269\pi$
$194$	5.24479	0.376554
$195$	2.11434	0.151411
$196$	17.0333	1.21666
$197$	−19.9274	−1.41976	−0.709882	−	0.704320i	$-0.751252\pi$
$197$	−19.9274	−1.41976	−0.709882	+	0.704320i	$0.751252\pi$
$198$	−2.89017	−0.205395
$199$	−13.1156	−0.929741	−0.464870	−	0.885379i	$-0.653899\pi$
$199$	−13.1156	−0.929741	−0.464870	+	0.885379i	$0.653899\pi$
$200$	1.00000	0.0707107
$201$	1.94517	0.137202
$202$	−2.40874	−0.169479
$203$	−11.2419	−0.789025
$204$	0.968804	0.0678298
$205$	10.0332	0.700746
$206$	10.6983	0.745382
$207$	10.3109	0.716659
$208$	−6.37989	−0.442365
$209$	−2.09641	−0.145012
$210$	−1.62468	−0.112114
$211$	−15.2695	−1.05120	−0.525599	−	0.850732i	$-0.676159\pi$
$211$	−15.2695	−1.05120	−0.525599	+	0.850732i	$0.676159\pi$
$212$	10.4014	0.714373
$213$	4.92031	0.337134
$214$	13.6952	0.936182
$215$	−7.00187	−0.477524
$216$	−1.95205	−0.132820
$217$	31.8704	2.16350
$218$	18.5167	1.25411
$219$	0.331408	0.0223944
$220$	−1.00000	−0.0674200
$221$	−18.6503	−1.25456
$222$	1.62752	0.109232
$223$	14.6456	0.980740	0.490370	−	0.871514i	$-0.336862\pi$
$223$	14.6456	0.980740	0.490370	+	0.871514i	$0.336862\pi$
$224$	4.90237	0.327554
$225$	−2.89017	−0.192678
$226$	−9.01739	−0.599828
$227$	15.6090	1.03600	0.518002	−	0.855380i	$-0.326676\pi$
$227$	15.6090	1.03600	0.518002	+	0.855380i	$0.326676\pi$
$228$	−0.694765	−0.0460120
$229$	11.4444	0.756265	0.378132	−	0.925752i	$-0.376566\pi$
$229$	11.4444	0.756265	0.378132	+	0.925752i	$0.376566\pi$
$230$	3.56759	0.235240
$231$	1.62468	0.106896
$232$	−2.29315	−0.150553
$233$	−3.45897	−0.226605	−0.113302	−	0.993561i	$-0.536143\pi$
$233$	−3.45897	−0.226605	−0.113302	+	0.993561i	$0.536143\pi$
$234$	18.4389	1.20539
$235$	−9.05617	−0.590759
$236$	13.4141	0.873181
$237$	−1.53508	−0.0997142
$238$	14.3311	0.928948
$239$	−15.1084	−0.977282	−0.488641	−	0.872485i	$-0.662507\pi$
$239$	−15.1084	−0.977282	−0.488641	+	0.872485i	$0.662507\pi$
$240$	−0.331408	−0.0213923
$241$	1.11549	0.0718552	0.0359276	−	0.999354i	$-0.488561\pi$
$241$	1.11549	0.0718552	0.0359276	+	0.999354i	$0.488561\pi$
$242$	1.00000	0.0642824
$243$	8.51522	0.546251
$244$	−1.92859	−0.123465
$245$	−17.0333	−1.08821
$246$	−3.32506	−0.211998
$247$	13.3748	0.851021
$248$	6.50101	0.412815
$249$	1.66043	0.105225
$250$	−1.00000	−0.0632456
$251$	19.2566	1.21546	0.607732	−	0.794142i	$-0.292079\pi$
$251$	19.2566	1.21546	0.607732	+	0.794142i	$0.292079\pi$
$252$	−14.1687	−0.892543
$253$	−3.56759	−0.224292
$254$	−13.9069	−0.872598
$255$	−0.968804	−0.0606689
$256$	1.00000	0.0625000
$257$	11.7238	0.731310	0.365655	−	0.930750i	$-0.380845\pi$
$257$	11.7238	0.731310	0.365655	+	0.930750i	$0.380845\pi$
$258$	2.32047	0.144466
$259$	24.0752	1.49596
$260$	6.37989	0.395664
$261$	6.62759	0.410237
$262$	−16.1976	−1.00069
$263$	−23.3143	−1.43762	−0.718809	−	0.695207i	$-0.755313\pi$
$263$	−23.3143	−1.43762	−0.718809	+	0.695207i	$0.755313\pi$
$264$	0.331408	0.0203967
$265$	−10.4014	−0.638955
$266$	−10.2774	−0.630146
$267$	1.55622	0.0952394
$268$	5.86942	0.358532
$269$	14.2787	0.870589	0.435295	−	0.900288i	$-0.356644\pi$
$269$	14.2787	0.870589	0.435295	+	0.900288i	$0.356644\pi$
$270$	1.95205	0.118798
$271$	−8.52229	−0.517692	−0.258846	−	0.965919i	$-0.583342\pi$
$271$	−8.52229	−0.517692	−0.258846	+	0.965919i	$0.583342\pi$
$272$	2.92330	0.177251
$273$	−10.3653	−0.627336
$274$	−12.5110	−0.755819
$275$	1.00000	0.0603023
$276$	−1.18233	−0.0711677
$277$	8.65060	0.519764	0.259882	−	0.965640i	$-0.416316\pi$
$277$	8.65060	0.519764	0.259882	+	0.965640i	$0.416316\pi$
$278$	−4.10209	−0.246027
$279$	−18.7890	−1.12487
$280$	−4.90237	−0.292973
$281$	−29.7933	−1.77732	−0.888661	−	0.458565i	$-0.848364\pi$
$281$	−29.7933	−1.77732	−0.888661	+	0.458565i	$0.848364\pi$
$282$	3.00128	0.178724
$283$	13.5317	0.804373	0.402187	−	0.915558i	$-0.368250\pi$
$283$	13.5317	0.804373	0.402187	+	0.915558i	$0.368250\pi$
$284$	14.8467	0.880991
$285$	0.694765	0.0411543
$286$	−6.37989	−0.377251
$287$	−49.1862	−2.90337
$288$	−2.89017	−0.170305
$289$	−8.45431	−0.497313
$290$	2.29315	0.134658
$291$	1.73816	0.101893
$292$	1.00000	0.0585206
$293$	−3.23533	−0.189010	−0.0945051	−	0.995524i	$-0.530127\pi$
$293$	−3.23533	−0.189010	−0.0945051	+	0.995524i	$0.530127\pi$
$294$	5.64495	0.329220
$295$	−13.4141	−0.780997
$296$	4.91092	0.285442
$297$	−1.95205	−0.113269
$298$	−11.4127	−0.661121
$299$	22.7608	1.31629
$300$	0.331408	0.0191338
$301$	34.3258	1.97851
$302$	−21.4371	−1.23357
$303$	−0.798276	−0.0458597
$304$	−2.09641	−0.120237
$305$	1.92859	0.110430
$306$	−8.44883	−0.482988
$307$	−15.3278	−0.874802	−0.437401	−	0.899266i	$-0.644101\pi$
$307$	−15.3278	−0.874802	−0.437401	+	0.899266i	$0.644101\pi$
$308$	4.90237	0.279339
$309$	3.54548	0.201695
$310$	−6.50101	−0.369233
$311$	−22.1365	−1.25525	−0.627623	−	0.778518i	$-0.715972\pi$
$311$	−22.1365	−1.25525	−0.627623	+	0.778518i	$0.715972\pi$
$312$	−2.11434	−0.119701
$313$	25.6250	1.44841	0.724205	−	0.689584i	$-0.242207\pi$
$313$	25.6250	1.44841	0.724205	+	0.689584i	$0.242207\pi$
$314$	5.76926	0.325578
$315$	14.1687	0.798315
$316$	−4.63200	−0.260571
$317$	14.5727	0.818482	0.409241	−	0.912426i	$-0.365794\pi$
$317$	14.5727	0.818482	0.409241	+	0.912426i	$0.365794\pi$
$318$	3.44711	0.193305
$319$	−2.29315	−0.128392
$320$	−1.00000	−0.0559017
$321$	4.53868	0.253325
$322$	−17.4896	−0.974660
$323$	−6.12843	−0.340995
$324$	8.02358	0.445755
$325$	−6.37989	−0.353892
$326$	−13.5070	−0.748086
$327$	6.13656	0.339353
$328$	−10.0332	−0.553988
$329$	44.3967	2.44767
$330$	−0.331408	−0.0182434
$331$	−7.11233	−0.390929	−0.195464	−	0.980711i	$-0.562621\pi$
$331$	−7.11233	−0.390929	−0.195464	+	0.980711i	$0.562621\pi$
$332$	5.01023	0.274972
$333$	−14.1934	−0.777794
$334$	−12.6024	−0.689574
$335$	−5.86942	−0.320681
$336$	1.62468	0.0886337
$337$	−8.89832	−0.484723	−0.242361	−	0.970186i	$-0.577922\pi$
$337$	−8.89832	−0.484723	−0.242361	+	0.970186i	$0.577922\pi$
$338$	27.7029	1.50684
$339$	−2.98843	−0.162309
$340$	−2.92330	−0.158538
$341$	6.50101	0.352050
$342$	6.05897	0.327632
$343$	49.1868	2.65584
$344$	7.00187	0.377516
$345$	1.18233	0.0636543
$346$	12.4322	0.668360
$347$	−4.20605	−0.225793	−0.112896	−	0.993607i	$-0.536013\pi$
$347$	−4.20605	−0.225793	−0.112896	+	0.993607i	$0.536013\pi$
$348$	−0.759967	−0.0407385
$349$	−7.36736	−0.394366	−0.197183	−	0.980367i	$-0.563179\pi$
$349$	−7.36736	−0.394366	−0.197183	+	0.980367i	$0.563179\pi$
$350$	4.90237	0.262043
$351$	12.4538	0.664736
$352$	1.00000	0.0533002
$353$	−22.5529	−1.20037	−0.600184	−	0.799862i	$-0.704906\pi$
$353$	−22.5529	−1.20037	−0.600184	+	0.799862i	$0.704906\pi$
$354$	4.44552	0.236277
$355$	−14.8467	−0.787982
$356$	4.69580	0.248877
$357$	4.74944	0.251367
$358$	26.4722	1.39910
$359$	14.8339	0.782904	0.391452	−	0.920198i	$-0.371973\pi$
$359$	14.8339	0.782904	0.391452	+	0.920198i	$0.371973\pi$
$360$	2.89017	0.152325
$361$	−14.6051	−0.768688
$362$	24.0587	1.26450
$363$	0.331408	0.0173944
$364$	−31.2766	−1.63934
$365$	−1.00000	−0.0523424
$366$	−0.639148	−0.0334088
$367$	11.5738	0.604145	0.302073	−	0.953285i	$-0.402321\pi$
$367$	11.5738	0.604145	0.302073	+	0.953285i	$0.402321\pi$
$368$	−3.56759	−0.185973
$369$	28.9975	1.50955
$370$	−4.91092	−0.255307
$371$	50.9917	2.64736
$372$	2.15449	0.111705
$373$	−31.7564	−1.64428	−0.822141	−	0.569283i	$-0.807221\pi$
$373$	−31.7564	−1.64428	−0.822141	+	0.569283i	$0.807221\pi$
$374$	2.92330	0.151160
$375$	−0.331408	−0.0171138
$376$	9.05617	0.467036
$377$	14.6300	0.753485
$378$	−9.56966	−0.492210
$379$	−34.9653	−1.79605	−0.898024	−	0.439947i	$-0.854997\pi$
$379$	−34.9653	−1.79605	−0.898024	+	0.439947i	$0.854997\pi$
$380$	2.09641	0.107543
$381$	−4.60886	−0.236119
$382$	−13.3900	−0.685091
$383$	−28.8266	−1.47297	−0.736485	−	0.676454i	$-0.763516\pi$
$383$	−28.8266	−1.47297	−0.736485	+	0.676454i	$0.763516\pi$
$384$	0.331408	0.0169121
$385$	−4.90237	−0.249848
$386$	11.9668	0.609093
$387$	−20.2366	−1.02868
$388$	5.24479	0.266264
$389$	−4.18391	−0.212133	−0.106066	−	0.994359i	$-0.533826\pi$
$389$	−4.18391	−0.212133	−0.106066	+	0.994359i	$0.533826\pi$
$390$	2.11434	0.107064
$391$	−10.4291	−0.527424
$392$	17.0333	0.860309
$393$	−5.36801	−0.270780
$394$	−19.9274	−1.00393
$395$	4.63200	0.233061
$396$	−2.89017	−0.145236
$397$	38.2890	1.92167	0.960834	−	0.277125i	$-0.0893818\pi$
$397$	38.2890	1.92167	0.960834	+	0.277125i	$0.0893818\pi$
$398$	−13.1156	−0.657426
$399$	−3.40600	−0.170513
$400$	1.00000	0.0500000
$401$	−5.93817	−0.296538	−0.148269	−	0.988947i	$-0.547370\pi$
$401$	−5.93817	−0.296538	−0.148269	+	0.988947i	$0.547370\pi$
$402$	1.94517	0.0970163
$403$	−41.4757	−2.06605
$404$	−2.40874	−0.119839
$405$	−8.02358	−0.398695
$406$	−11.2419	−0.557925
$407$	4.91092	0.243426
$408$	0.968804	0.0479629
$409$	13.1565	0.650548	0.325274	−	0.945620i	$-0.394543\pi$
$409$	13.1565	0.650548	0.325274	+	0.945620i	$0.394543\pi$
$410$	10.0332	0.495502
$411$	−4.14625	−0.204520
$412$	10.6983	0.527065
$413$	65.7607	3.23587
$414$	10.3109	0.506755
$415$	−5.01023	−0.245942
$416$	−6.37989	−0.312800
$417$	−1.35946	−0.0665732
$418$	−2.09641	−0.102539
$419$	−21.3037	−1.04075	−0.520376	−	0.853937i	$-0.674208\pi$
$419$	−21.3037	−1.04075	−0.520376	+	0.853937i	$0.674208\pi$
$420$	−1.62468	−0.0792764
$421$	−8.96160	−0.436761	−0.218381	−	0.975864i	$-0.570077\pi$
$421$	−8.96160	−0.436761	−0.218381	+	0.975864i	$0.570077\pi$
$422$	−15.2695	−0.743309
$423$	−26.1739	−1.27262
$424$	10.4014	0.505138
$425$	2.92330	0.141801
$426$	4.92031	0.238390
$427$	−9.45465	−0.457542
$428$	13.6952	0.661981
$429$	−2.11434	−0.102081
$430$	−7.00187	−0.337660
$431$	29.3112	1.41187	0.705936	−	0.708276i	$-0.250527\pi$
$431$	29.3112	1.41187	0.705936	+	0.708276i	$0.250527\pi$
$432$	−1.95205	−0.0939179
$433$	−6.68970	−0.321486	−0.160743	−	0.986996i	$-0.551389\pi$
$433$	−6.68970	−0.321486	−0.160743	+	0.986996i	$0.551389\pi$
$434$	31.8704	1.52983
$435$	0.759967	0.0364376
$436$	18.5167	0.886787
$437$	7.47912	0.357775
$438$	0.331408	0.0158353
$439$	−10.7928	−0.515114	−0.257557	−	0.966263i	$-0.582917\pi$
$439$	−10.7928	−0.515114	−0.257557	+	0.966263i	$0.582917\pi$
$440$	−1.00000	−0.0476731
$441$	−49.2290	−2.34424
$442$	−18.6503	−0.887105
$443$	−22.7422	−1.08051	−0.540257	−	0.841500i	$-0.681673\pi$
$443$	−22.7422	−1.08051	−0.540257	+	0.841500i	$0.681673\pi$
$444$	1.62752	0.0772386
$445$	−4.69580	−0.222602
$446$	14.6456	0.693488
$447$	−3.78226	−0.178895
$448$	4.90237	0.231615
$449$	−38.8738	−1.83457	−0.917284	−	0.398234i	$-0.869623\pi$
$449$	−38.8738	−1.83457	−0.917284	+	0.398234i	$0.869623\pi$
$450$	−2.89017	−0.136244
$451$	−10.0332	−0.472443
$452$	−9.01739	−0.424142
$453$	−7.10442	−0.333795
$454$	15.6090	0.732565
$455$	31.2766	1.46627
$456$	−0.694765	−0.0325354
$457$	26.2544	1.22813	0.614065	−	0.789255i	$-0.289533\pi$
$457$	26.2544	1.22813	0.614065	+	0.789255i	$0.289533\pi$
$458$	11.4444	0.534760
$459$	−5.70642	−0.266353
$460$	3.56759	0.166340
$461$	−6.86984	−0.319960	−0.159980	−	0.987120i	$-0.551143\pi$
$461$	−6.86984	−0.319960	−0.159980	+	0.987120i	$0.551143\pi$
$462$	1.62468	0.0755871
$463$	36.3648	1.69001	0.845007	−	0.534755i	$-0.179596\pi$
$463$	36.3648	1.69001	0.845007	+	0.534755i	$0.179596\pi$
$464$	−2.29315	−0.106457
$465$	−2.15449	−0.0999119
$466$	−3.45897	−0.160234
$467$	14.5768	0.674534	0.337267	−	0.941409i	$-0.390498\pi$
$467$	14.5768	0.674534	0.337267	+	0.941409i	$0.390498\pi$
$468$	18.4389	0.852341
$469$	28.7741	1.32866
$470$	−9.05617	−0.417730
$471$	1.91198	0.0880992
$472$	13.4141	0.617432
$473$	7.00187	0.321946
$474$	−1.53508	−0.0705086
$475$	−2.09641	−0.0961898
$476$	14.3311	0.656865
$477$	−30.0619	−1.37644
$478$	−15.1084	−0.691043
$479$	−42.1850	−1.92748	−0.963741	−	0.266841i	$-0.914020\pi$
$479$	−42.1850	−1.92748	−0.963741	+	0.266841i	$0.914020\pi$
$480$	−0.331408	−0.0151266
$481$	−31.3311	−1.42858
$482$	1.11549	0.0508093
$483$	−5.79620	−0.263736
$484$	1.00000	0.0454545
$485$	−5.24479	−0.238154
$486$	8.51522	0.386258
$487$	14.5820	0.660774	0.330387	−	0.943845i	$-0.392821\pi$
$487$	14.5820	0.660774	0.330387	+	0.943845i	$0.392821\pi$
$488$	−1.92859	−0.0873030
$489$	−4.47634	−0.202427
$490$	−17.0333	−0.769484
$491$	12.8775	0.581155	0.290577	−	0.956851i	$-0.406153\pi$
$491$	12.8775	0.581155	0.290577	+	0.956851i	$0.406153\pi$
$492$	−3.32506	−0.149905
$493$	−6.70356	−0.301913
$494$	13.3748	0.601762
$495$	2.89017	0.129903
$496$	6.50101	0.291904
$497$	72.7841	3.26482
$498$	1.66043	0.0744055
$499$	0.603112	0.0269990	0.0134995	−	0.999909i	$-0.495703\pi$
$499$	0.603112	0.0269990	0.0134995	+	0.999909i	$0.495703\pi$
$500$	−1.00000	−0.0447214
$501$	−4.17654	−0.186594
$502$	19.2566	0.859463
$503$	9.05358	0.403679	0.201839	−	0.979419i	$-0.435308\pi$
$503$	9.05358	0.403679	0.201839	+	0.979419i	$0.435308\pi$
$504$	−14.1687	−0.631123
$505$	2.40874	0.107188
$506$	−3.56759	−0.158599
$507$	9.18096	0.407741
$508$	−13.9069	−0.617020
$509$	10.7116	0.474783	0.237391	−	0.971414i	$-0.423708\pi$
$509$	10.7116	0.474783	0.237391	+	0.971414i	$0.423708\pi$
$510$	−0.968804	−0.0428994
$511$	4.90237	0.216868
$512$	1.00000	0.0441942
$513$	4.09228	0.180679
$514$	11.7238	0.517115
$515$	−10.6983	−0.471421
$516$	2.32047	0.102153
$517$	9.05617	0.398290
$518$	24.0752	1.05780
$519$	4.12013	0.180854
$520$	6.37989	0.279776
$521$	−9.83489	−0.430874	−0.215437	−	0.976518i	$-0.569118\pi$
$521$	−9.83489	−0.430874	−0.215437	+	0.976518i	$0.569118\pi$
$522$	6.62759	0.290082
$523$	10.7932	0.471954	0.235977	−	0.971759i	$-0.424171\pi$
$523$	10.7932	0.471954	0.235977	+	0.971759i	$0.424171\pi$
$524$	−16.1976	−0.707595
$525$	1.62468	0.0709070
$526$	−23.3143	−1.01655
$527$	19.0044	0.827846
$528$	0.331408	0.0144227
$529$	−10.2723	−0.446622
$530$	−10.4014	−0.451809
$531$	−38.7689	−1.68243
$532$	−10.2774	−0.445581
$533$	64.0104	2.77260
$534$	1.55622	0.0673444
$535$	−13.6952	−0.592094
$536$	5.86942	0.253520
$537$	8.77310	0.378587
$538$	14.2787	0.615600
$539$	17.0333	0.733674
$540$	1.95205	0.0840027
$541$	7.02125	0.301867	0.150933	−	0.988544i	$-0.451772\pi$
$541$	7.02125	0.301867	0.150933	+	0.988544i	$0.451772\pi$
$542$	−8.52229	−0.366064
$543$	7.97325	0.342165
$544$	2.92330	0.125335
$545$	−18.5167	−0.793167
$546$	−10.3653	−0.443594
$547$	−25.2070	−1.07777	−0.538887	−	0.842378i	$-0.681155\pi$
$547$	−25.2070	−1.07777	−0.538887	+	0.842378i	$0.681155\pi$
$548$	−12.5110	−0.534445
$549$	5.57394	0.237890
$550$	1.00000	0.0426401
$551$	4.80737	0.204801
$552$	−1.18233	−0.0503231
$553$	−22.7078	−0.965634
$554$	8.65060	0.367529
$555$	−1.62752	−0.0690843
$556$	−4.10209	−0.173967
$557$	32.9771	1.39728	0.698642	−	0.715472i	$-0.253788\pi$
$557$	32.9771	1.39728	0.698642	+	0.715472i	$0.253788\pi$
$558$	−18.7890	−0.795403
$559$	−44.6711	−1.88939
$560$	−4.90237	−0.207163
$561$	0.968804	0.0409029
$562$	−29.7933	−1.25676
$563$	2.51296	0.105909	0.0529544	−	0.998597i	$-0.483136\pi$
$563$	2.51296	0.105909	0.0529544	+	0.998597i	$0.483136\pi$
$564$	3.00128	0.126377
$565$	9.01739	0.379364
$566$	13.5317	0.568778
$567$	39.3346	1.65190
$568$	14.8467	0.622954
$569$	−22.6819	−0.950874	−0.475437	−	0.879750i	$-0.657710\pi$
$569$	−22.6819	−0.950874	−0.475437	+	0.879750i	$0.657710\pi$
$570$	0.694765	0.0291005
$571$	45.4080	1.90027	0.950134	−	0.311842i	$-0.100946\pi$
$571$	45.4080	1.90027	0.950134	+	0.311842i	$0.100946\pi$
$572$	−6.37989	−0.266756
$573$	−4.43754	−0.185381
$574$	−49.1862	−2.05299
$575$	−3.56759	−0.148779
$576$	−2.89017	−0.120424
$577$	−17.2598	−0.718535	−0.359267	−	0.933235i	$-0.616973\pi$
$577$	−17.2598	−0.718535	−0.359267	+	0.933235i	$0.616973\pi$
$578$	−8.45431	−0.351653
$579$	3.96588	0.164816
$580$	2.29315	0.0952178
$581$	24.5620	1.01900
$582$	1.73816	0.0720492
$583$	10.4014	0.430783
$584$	1.00000	0.0413803
$585$	−18.4389	−0.762357
$586$	−3.23533	−0.133650
$587$	22.2844	0.919777	0.459888	−	0.887977i	$-0.347889\pi$
$587$	22.2844	0.919777	0.459888	+	0.887977i	$0.347889\pi$
$588$	5.64495	0.232794
$589$	−13.6288	−0.561564
$590$	−13.4141	−0.552248
$591$	−6.60407	−0.271655
$592$	4.91092	0.201838
$593$	27.2278	1.11811	0.559056	−	0.829130i	$-0.311164\pi$
$593$	27.2278	1.11811	0.559056	+	0.829130i	$0.311164\pi$
$594$	−1.95205	−0.0800934
$595$	−14.3311	−0.587518
$596$	−11.4127	−0.467483
$597$	−4.34661	−0.177895
$598$	22.7608	0.930759
$599$	23.4079	0.956421	0.478210	−	0.878245i	$-0.341286\pi$
$599$	23.4079	0.956421	0.478210	+	0.878245i	$0.341286\pi$
$600$	0.331408	0.0135297
$601$	15.6714	0.639252	0.319626	−	0.947544i	$-0.396443\pi$
$601$	15.6714	0.639252	0.319626	+	0.947544i	$0.396443\pi$
$602$	34.3258	1.39901
$603$	−16.9636	−0.690812
$604$	−21.4371	−0.872264
$605$	−1.00000	−0.0406558
$606$	−0.798276	−0.0324277
$607$	−5.23655	−0.212545	−0.106273	−	0.994337i	$-0.533892\pi$
$607$	−5.23655	−0.212545	−0.106273	+	0.994337i	$0.533892\pi$
$608$	−2.09641	−0.0850205
$609$	−3.72564	−0.150971
$610$	1.92859	0.0780861
$611$	−57.7773	−2.33742
$612$	−8.44883	−0.341524
$613$	21.0082	0.848512	0.424256	−	0.905542i	$-0.360536\pi$
$613$	21.0082	0.848512	0.424256	+	0.905542i	$0.360536\pi$
$614$	−15.3278	−0.618579
$615$	3.32506	0.134079
$616$	4.90237	0.197522
$617$	26.9010	1.08299	0.541496	−	0.840703i	$-0.317858\pi$
$617$	26.9010	1.08299	0.541496	+	0.840703i	$0.317858\pi$
$618$	3.54548	0.142620
$619$	19.4060	0.779992	0.389996	−	0.920817i	$-0.372476\pi$
$619$	19.4060	0.779992	0.389996	+	0.920817i	$0.372476\pi$
$620$	−6.50101	−0.261087
$621$	6.96410	0.279460
$622$	−22.1365	−0.887593
$623$	23.0206	0.922300
$624$	−2.11434	−0.0846414
$625$	1.00000	0.0400000
$626$	25.6250	1.02418
$627$	−0.694765	−0.0277463
$628$	5.76926	0.230218
$629$	14.3561	0.572416
$630$	14.1687	0.564494
$631$	5.54615	0.220789	0.110394	−	0.993888i	$-0.464789\pi$
$631$	5.54615	0.220789	0.110394	+	0.993888i	$0.464789\pi$
$632$	−4.63200	−0.184251
$633$	−5.06044	−0.201134
$634$	14.5727	0.578754
$635$	13.9069	0.551879
$636$	3.44711	0.136687
$637$	−108.670	−4.30567
$638$	−2.29315	−0.0907866
$639$	−42.9095	−1.69747
$640$	−1.00000	−0.0395285
$641$	46.8120	1.84896	0.924482	−	0.381225i	$-0.124498\pi$
$641$	46.8120	1.84896	0.924482	+	0.381225i	$0.124498\pi$
$642$	4.53868	0.179127
$643$	−5.51980	−0.217680	−0.108840	−	0.994059i	$-0.534714\pi$
$643$	−5.51980	−0.217680	−0.108840	+	0.994059i	$0.534714\pi$
$644$	−17.4896	−0.689189
$645$	−2.32047	−0.0913685
$646$	−6.12843	−0.241120
$647$	−11.2691	−0.443033	−0.221517	−	0.975157i	$-0.571101\pi$
$647$	−11.2691	−0.443033	−0.221517	+	0.975157i	$0.571101\pi$
$648$	8.02358	0.315196
$649$	13.4141	0.526548
$650$	−6.37989	−0.250240
$651$	10.5621	0.413961
$652$	−13.5070	−0.528977
$653$	0.550615	0.0215472	0.0107736	−	0.999942i	$-0.496571\pi$
$653$	0.550615	0.0215472	0.0107736	+	0.999942i	$0.496571\pi$
$654$	6.13656	0.239959
$655$	16.1976	0.632892
$656$	−10.0332	−0.391729
$657$	−2.89017	−0.112756
$658$	44.3967	1.73076
$659$	−42.8037	−1.66740	−0.833698	−	0.552221i	$-0.813781\pi$
$659$	−42.8037	−1.66740	−0.833698	+	0.552221i	$0.813781\pi$
$660$	−0.331408	−0.0129000
$661$	−7.67853	−0.298660	−0.149330	−	0.988787i	$-0.547712\pi$
$661$	−7.67853	−0.298660	−0.149330	+	0.988787i	$0.547712\pi$
$662$	−7.11233	−0.276429
$663$	−6.18086	−0.240045
$664$	5.01023	0.194435
$665$	10.2774	0.398539
$666$	−14.1934	−0.549983
$667$	8.18101	0.316770
$668$	−12.6024	−0.487602
$669$	4.85365	0.187653
$670$	−5.86942	−0.226756
$671$	−1.92859	−0.0744522
$672$	1.62468	0.0626735
$673$	6.35521	0.244975	0.122488	−	0.992470i	$-0.460913\pi$
$673$	6.35521	0.244975	0.122488	+	0.992470i	$0.460913\pi$
$674$	−8.89832	−0.342751
$675$	−1.95205	−0.0751343
$676$	27.7029	1.06550
$677$	−11.7067	−0.449924	−0.224962	−	0.974368i	$-0.572226\pi$
$677$	−11.7067	−0.449924	−0.224962	+	0.974368i	$0.572226\pi$
$678$	−2.98843	−0.114770
$679$	25.7119	0.986733
$680$	−2.92330	−0.112103
$681$	5.17293	0.198227
$682$	6.50101	0.248937
$683$	−0.825607	−0.0315910	−0.0157955	−	0.999875i	$-0.505028\pi$
$683$	−0.825607	−0.0315910	−0.0157955	+	0.999875i	$0.505028\pi$
$684$	6.05897	0.231671
$685$	12.5110	0.478022
$686$	49.1868	1.87796
$687$	3.79275	0.144702
$688$	7.00187	0.266944
$689$	−66.3599	−2.52811
$690$	1.18233	0.0450104
$691$	−33.6741	−1.28102	−0.640512	−	0.767948i	$-0.721278\pi$
$691$	−33.6741	−1.28102	−0.640512	+	0.767948i	$0.721278\pi$
$692$	12.4322	0.472602
$693$	−14.1687	−0.538224
$694$	−4.20605	−0.159659
$695$	4.10209	0.155601
$696$	−0.759967	−0.0288065
$697$	−29.3299	−1.11095
$698$	−7.36736	−0.278859
$699$	−1.14633	−0.0433581
$700$	4.90237	0.185292
$701$	−4.17261	−0.157597	−0.0787986	−	0.996891i	$-0.525108\pi$
$701$	−4.17261	−0.157597	−0.0787986	+	0.996891i	$0.525108\pi$
$702$	12.4538	0.470040
$703$	−10.2953	−0.388295
$704$	1.00000	0.0376889
$705$	−3.00128	−0.113035
$706$	−22.5529	−0.848789
$707$	−11.8086	−0.444106
$708$	4.44552	0.167073
$709$	3.15539	0.118503	0.0592516	−	0.998243i	$-0.481129\pi$
$709$	3.15539	0.118503	0.0592516	+	0.998243i	$0.481129\pi$
$710$	−14.8467	−0.557187
$711$	13.3873	0.502062
$712$	4.69580	0.175983
$713$	−23.1929	−0.868583
$714$	4.74944	0.177743
$715$	6.37989	0.238594
$716$	26.4722	0.989314
$717$	−5.00704	−0.186991
$718$	14.8339	0.553597
$719$	−24.8465	−0.926619	−0.463309	−	0.886197i	$-0.653338\pi$
$719$	−24.8465	−0.926619	−0.463309	+	0.886197i	$0.653338\pi$
$720$	2.89017	0.107710
$721$	52.4468	1.95322
$722$	−14.6051	−0.543545
$723$	0.369683	0.0137486
$724$	24.0587	0.894136
$725$	−2.29315	−0.0851654
$726$	0.331408	0.0122997
$727$	−22.3653	−0.829485	−0.414742	−	0.909939i	$-0.636128\pi$
$727$	−22.3653	−0.829485	−0.414742	+	0.909939i	$0.636128\pi$
$728$	−31.2766	−1.15919
$729$	−21.2487	−0.786991
$730$	−1.00000	−0.0370117
$731$	20.4686	0.757058
$732$	−0.639148	−0.0236236
$733$	39.9866	1.47694	0.738470	−	0.674287i	$-0.235549\pi$
$733$	39.9866	1.47694	0.738470	+	0.674287i	$0.235549\pi$
$734$	11.5738	0.427195
$735$	−5.64495	−0.208217
$736$	−3.56759	−0.131503
$737$	5.86942	0.216203
$738$	28.9975	1.06741
$739$	29.4299	1.08260	0.541298	−	0.840831i	$-0.317933\pi$
$739$	29.4299	1.08260	0.541298	+	0.840831i	$0.317933\pi$
$740$	−4.91092	−0.180529
$741$	4.43252	0.162833
$742$	50.9917	1.87196
$743$	−18.0718	−0.662991	−0.331495	−	0.943457i	$-0.607553\pi$
$743$	−18.0718	−0.662991	−0.331495	+	0.943457i	$0.607553\pi$
$744$	2.15449	0.0789873
$745$	11.4127	0.418129
$746$	−31.7564	−1.16268
$747$	−14.4804	−0.529810
$748$	2.92330	0.106886
$749$	67.1388	2.45320
$750$	−0.331408	−0.0121013
$751$	−10.5799	−0.386066	−0.193033	−	0.981192i	$-0.561832\pi$
$751$	−10.5799	−0.386066	−0.193033	+	0.981192i	$0.561832\pi$
$752$	9.05617	0.330245
$753$	6.38178	0.232565
$754$	14.6300	0.532794
$755$	21.4371	0.780177
$756$	−9.56966	−0.348045
$757$	22.0963	0.803103	0.401551	−	0.915837i	$-0.368471\pi$
$757$	22.0963	0.803103	0.401551	+	0.915837i	$0.368471\pi$
$758$	−34.9653	−1.27000
$759$	−1.18233	−0.0429157
$760$	2.09641	0.0760447
$761$	−10.6269	−0.385226	−0.192613	−	0.981275i	$-0.561696\pi$
$761$	−10.6269	−0.385226	−0.192613	+	0.981275i	$0.561696\pi$
$762$	−4.60886	−0.166961
$763$	90.7756	3.28630
$764$	−13.3900	−0.484432
$765$	8.44883	0.305468
$766$	−28.8266	−1.04155
$767$	−85.5802	−3.09012
$768$	0.331408	0.0119586
$769$	37.3841	1.34810	0.674052	−	0.738684i	$-0.264552\pi$
$769$	37.3841	1.34810	0.674052	+	0.738684i	$0.264552\pi$
$770$	−4.90237	−0.176669
$771$	3.88536	0.139928
$772$	11.9668	0.430694
$773$	0.428296	0.0154047	0.00770237	−	0.999970i	$-0.497548\pi$
$773$	0.428296	0.0154047	0.00770237	+	0.999970i	$0.497548\pi$
$774$	−20.2366	−0.727389
$775$	6.50101	0.233523
$776$	5.24479	0.188277
$777$	7.97870	0.286234
$778$	−4.18391	−0.150001
$779$	21.0336	0.753606
$780$	2.11434	0.0757056
$781$	14.8467	0.531257
$782$	−10.4291	−0.372945
$783$	4.47633	0.159971
$784$	17.0333	0.608331
$785$	−5.76926	−0.205914
$786$	−5.36801	−0.191470
$787$	−4.09940	−0.146128	−0.0730639	−	0.997327i	$-0.523278\pi$
$787$	−4.09940	−0.146128	−0.0730639	+	0.997327i	$0.523278\pi$
$788$	−19.9274	−0.709882
$789$	−7.72652	−0.275071
$790$	4.63200	0.164799
$791$	−44.2066	−1.57181
$792$	−2.89017	−0.102698
$793$	12.3042	0.436933
$794$	38.2890	1.35882
$795$	−3.44711	−0.122257
$796$	−13.1156	−0.464870
$797$	24.5018	0.867900	0.433950	−	0.900937i	$-0.357119\pi$
$797$	24.5018	0.867900	0.433950	+	0.900937i	$0.357119\pi$
$798$	−3.40600	−0.120571
$799$	26.4739	0.936579
$800$	1.00000	0.0353553
$801$	−13.5717	−0.479531
$802$	−5.93817	−0.209684
$803$	1.00000	0.0352892
$804$	1.94517	0.0686009
$805$	17.4896	0.616429
$806$	−41.4757	−1.46092
$807$	4.73208	0.166577
$808$	−2.40874	−0.0847393
$809$	15.8200	0.556200	0.278100	−	0.960552i	$-0.410295\pi$
$809$	15.8200	0.556200	0.278100	+	0.960552i	$0.410295\pi$
$810$	−8.02358	−0.281920
$811$	3.95320	0.138816	0.0694078	−	0.997588i	$-0.477889\pi$
$811$	3.95320	0.138816	0.0694078	+	0.997588i	$0.477889\pi$
$812$	−11.2419	−0.394512
$813$	−2.82435	−0.0990543
$814$	4.91092	0.172128
$815$	13.5070	0.473131
$816$	0.968804	0.0339149
$817$	−14.6788	−0.513545
$818$	13.1565	0.460007
$819$	90.3946	3.15864
$820$	10.0332	0.350373
$821$	32.6498	1.13949	0.569743	−	0.821823i	$-0.307043\pi$
$821$	32.6498	1.13949	0.569743	+	0.821823i	$0.307043\pi$
$822$	−4.14625	−0.144617
$823$	35.8261	1.24882	0.624410	−	0.781096i	$-0.285339\pi$
$823$	35.8261	1.24882	0.624410	+	0.781096i	$0.285339\pi$
$824$	10.6983	0.372691
$825$	0.331408	0.0115381
$826$	65.7607	2.28811
$827$	11.8140	0.410814	0.205407	−	0.978677i	$-0.434148\pi$
$827$	11.8140	0.410814	0.205407	+	0.978677i	$0.434148\pi$
$828$	10.3109	0.358330
$829$	−15.4970	−0.538233	−0.269116	−	0.963108i	$-0.586732\pi$
$829$	−15.4970	−0.538233	−0.269116	+	0.963108i	$0.586732\pi$
$830$	−5.01023	−0.173908
$831$	2.86687	0.0994507
$832$	−6.37989	−0.221183
$833$	49.7933	1.72524
$834$	−1.35946	−0.0470744
$835$	12.6024	0.436125
$836$	−2.09641	−0.0725058
$837$	−12.6903	−0.438640
$838$	−21.3037	−0.735923
$839$	−45.5236	−1.57165	−0.785824	−	0.618450i	$-0.787761\pi$
$839$	−45.5236	−1.57165	−0.785824	+	0.618450i	$0.787761\pi$
$840$	−1.62468	−0.0560569
$841$	−23.7415	−0.818671
$842$	−8.96160	−0.308837
$843$	−9.87374	−0.340070
$844$	−15.2695	−0.525599
$845$	−27.7029	−0.953010
$846$	−26.1739	−0.899876
$847$	4.90237	0.168448
$848$	10.4014	0.357187
$849$	4.48449	0.153907
$850$	2.92330	0.100268
$851$	−17.5202	−0.600583
$852$	4.92031	0.168567
$853$	−22.8485	−0.782318	−0.391159	−	0.920323i	$-0.627926\pi$
$853$	−22.8485	−0.782318	−0.391159	+	0.920323i	$0.627926\pi$
$854$	−9.45465	−0.323531
$855$	−6.05897	−0.207212
$856$	13.6952	0.468091
$857$	−15.4585	−0.528053	−0.264026	−	0.964515i	$-0.585051\pi$
$857$	−15.4585	−0.528053	−0.264026	+	0.964515i	$0.585051\pi$
$858$	−2.11434	−0.0721825
$859$	45.9257	1.56697	0.783483	−	0.621413i	$-0.213441\pi$
$859$	45.9257	1.56697	0.783483	+	0.621413i	$0.213441\pi$
$860$	−7.00187	−0.238762
$861$	−16.3007	−0.555526
$862$	29.3112	0.998344
$863$	−3.89457	−0.132573	−0.0662864	−	0.997801i	$-0.521115\pi$
$863$	−3.89457	−0.132573	−0.0662864	+	0.997801i	$0.521115\pi$
$864$	−1.95205	−0.0664100
$865$	−12.4322	−0.422708
$866$	−6.68970	−0.227325
$867$	−2.80182	−0.0951549
$868$	31.8704	1.08175
$869$	−4.63200	−0.157130
$870$	0.759967	0.0257653
$871$	−37.4463	−1.26882
$872$	18.5167	0.627053
$873$	−15.1583	−0.513032
$874$	7.47912	0.252985
$875$	−4.90237	−0.165730
$876$	0.331408	0.0111972
$877$	19.0282	0.642535	0.321268	−	0.946988i	$-0.395891\pi$
$877$	19.0282	0.642535	0.321268	+	0.946988i	$0.395891\pi$
$878$	−10.7928	−0.364240
$879$	−1.07221	−0.0361649
$880$	−1.00000	−0.0337100
$881$	33.5735	1.13112	0.565560	−	0.824707i	$-0.308660\pi$
$881$	33.5735	1.13112	0.565560	+	0.824707i	$0.308660\pi$
$882$	−49.2290	−1.65763
$883$	−39.5276	−1.33021	−0.665105	−	0.746750i	$-0.731613\pi$
$883$	−39.5276	−1.33021	−0.665105	+	0.746750i	$0.731613\pi$
$884$	−18.6503	−0.627278
$885$	−4.44552	−0.149435
$886$	−22.7422	−0.764039
$887$	16.2400	0.545286	0.272643	−	0.962115i	$-0.412102\pi$
$887$	16.2400	0.545286	0.272643	+	0.962115i	$0.412102\pi$
$888$	1.62752	0.0546159
$889$	−68.1769	−2.28658
$890$	−4.69580	−0.157404
$891$	8.02358	0.268800
$892$	14.6456	0.490370
$893$	−18.9854	−0.635323
$894$	−3.78226	−0.126498
$895$	−26.4722	−0.884869
$896$	4.90237	0.163777
$897$	7.54310	0.251857
$898$	−38.8738	−1.29724
$899$	−14.9078	−0.497203
$900$	−2.89017	−0.0963390
$901$	30.4065	1.01299
$902$	−10.0332	−0.334067
$903$	11.3758	0.378564
$904$	−9.01739	−0.299914
$905$	−24.0587	−0.799740
$906$	−7.10442	−0.236029
$907$	38.5573	1.28027	0.640137	−	0.768261i	$-0.278878\pi$
$907$	38.5573	1.28027	0.640137	+	0.768261i	$0.278878\pi$
$908$	15.6090	0.518002
$909$	6.96167	0.230904
$910$	31.2766	1.03681
$911$	27.3037	0.904613	0.452307	−	0.891862i	$-0.350601\pi$
$911$	27.3037	0.904613	0.452307	+	0.891862i	$0.350601\pi$
$912$	−0.694765	−0.0230060
$913$	5.01023	0.165814
$914$	26.2544	0.868419
$915$	0.639148	0.0211296
$916$	11.4444	0.378132
$917$	−79.4067	−2.62224
$918$	−5.70642	−0.188340
$919$	−21.1407	−0.697367	−0.348683	−	0.937241i	$-0.613371\pi$
$919$	−21.1407	−0.697367	−0.348683	+	0.937241i	$0.613371\pi$
$920$	3.56759	0.117620
$921$	−5.07974	−0.167383
$922$	−6.86984	−0.226246
$923$	−94.7204	−3.11776
$924$	1.62468	0.0534482
$925$	4.91092	0.161470
$926$	36.3648	1.19502
$927$	−30.9198	−1.01554
$928$	−2.29315	−0.0752763
$929$	22.3021	0.731708	0.365854	−	0.930672i	$-0.380777\pi$
$929$	22.3021	0.731708	0.365854	+	0.930672i	$0.380777\pi$
$930$	−2.15449	−0.0706484
$931$	−35.7086	−1.17030
$932$	−3.45897	−0.113302
$933$	−7.33620	−0.240176
$934$	14.5768	0.476967
$935$	−2.92330	−0.0956021
$936$	18.4389	0.602696
$937$	−35.6217	−1.16371	−0.581856	−	0.813292i	$-0.697673\pi$
$937$	−35.6217	−1.16371	−0.581856	+	0.813292i	$0.697673\pi$
$938$	28.7741	0.939508
$939$	8.49232	0.277136
$940$	−9.05617	−0.295380
$941$	−30.6619	−0.999551	−0.499775	−	0.866155i	$-0.666584\pi$
$941$	−30.6619	−0.999551	−0.499775	+	0.866155i	$0.666584\pi$
$942$	1.91198	0.0622955
$943$	35.7942	1.16562
$944$	13.4141	0.436591
$945$	9.56966	0.311301
$946$	7.00187	0.227650
$947$	−51.5259	−1.67437	−0.837183	−	0.546922i	$-0.815799\pi$
$947$	−51.5259	−1.67437	−0.837183	+	0.546922i	$0.815799\pi$
$948$	−1.53508	−0.0498571
$949$	−6.37989	−0.207100
$950$	−2.09641	−0.0680164
$951$	4.82949	0.156607
$952$	14.3311	0.464474
$953$	−45.6140	−1.47758	−0.738792	−	0.673934i	$-0.764603\pi$
$953$	−45.6140	−1.47758	−0.738792	+	0.673934i	$0.764603\pi$
$954$	−30.0619	−0.973290
$955$	13.3900	0.433289
$956$	−15.1084	−0.488641
$957$	−0.759967	−0.0245662
$958$	−42.1850	−1.36294
$959$	−61.3338	−1.98057
$960$	−0.331408	−0.0106961
$961$	11.2632	0.363329
$962$	−31.3311	−1.01016
$963$	−39.5813	−1.27549
$964$	1.11549	0.0359276
$965$	−11.9668	−0.385224
$966$	−5.79620	−0.186490
$967$	−35.3987	−1.13834	−0.569172	−	0.822218i	$-0.692736\pi$
$967$	−35.3987	−1.13834	−0.569172	+	0.822218i	$0.692736\pi$
$968$	1.00000	0.0321412
$969$	−2.03101	−0.0652454
$970$	−5.24479	−0.168400
$971$	43.6959	1.40227	0.701134	−	0.713029i	$-0.252677\pi$
$971$	43.6959	1.40227	0.701134	+	0.713029i	$0.252677\pi$
$972$	8.51522	0.273126
$973$	−20.1100	−0.644696
$974$	14.5820	0.467238
$975$	−2.11434	−0.0677131
$976$	−1.92859	−0.0617325
$977$	−43.5923	−1.39464	−0.697320	−	0.716759i	$-0.745625\pi$
$977$	−43.5923	−1.39464	−0.697320	+	0.716759i	$0.745625\pi$
$978$	−4.47634	−0.143137
$979$	4.69580	0.150079
$980$	−17.0333	−0.544107
$981$	−53.5163	−1.70864
$982$	12.8775	0.410939
$983$	0.632120	0.0201615	0.0100807	−	0.999949i	$-0.496791\pi$
$983$	0.632120	0.0201615	0.0100807	+	0.999949i	$0.496791\pi$
$984$	−3.32506	−0.105999
$985$	19.9274	0.634938
$986$	−6.70356	−0.213485
$987$	14.7134	0.468333
$988$	13.3748	0.425510
$989$	−24.9798	−0.794311
$990$	2.89017	0.0918556
$991$	11.9498	0.379599	0.189799	−	0.981823i	$-0.439216\pi$
$991$	11.9498	0.379599	0.189799	+	0.981823i	$0.439216\pi$
$992$	6.50101	0.206407
$993$	−2.35708	−0.0747997
$994$	72.7841	2.30857
$995$	13.1156	0.415793
$996$	1.66043	0.0526126
$997$	5.42609	0.171846	0.0859229	−	0.996302i	$-0.472616\pi$
$997$	5.42609	0.171846	0.0859229	+	0.996302i	$0.472616\pi$
$998$	0.603112	0.0190912
$999$	−9.58635	−0.303299

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bd.1.7	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bd.1.7	✓	14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.331408 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.331408 q^{6} +4.90237 q^{7} +1.00000 q^{8} -2.89017 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.331408 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.331408 q^{6} +4.90237 q^{7} +1.00000 q^{8} -2.89017 q^{9} -1.00000 q^{10} +1.00000 q^{11} +0.331408 q^{12} -6.37989 q^{13} +4.90237 q^{14} -0.331408 q^{15} +1.00000 q^{16} +2.92330 q^{17} -2.89017 q^{18} -2.09641 q^{19} -1.00000 q^{20} +1.62468 q^{21} +1.00000 q^{22} -3.56759 q^{23} +0.331408 q^{24} +1.00000 q^{25} -6.37989 q^{26} -1.95205 q^{27} +4.90237 q^{28} -2.29315 q^{29} -0.331408 q^{30} +6.50101 q^{31} +1.00000 q^{32} +0.331408 q^{33} +2.92330 q^{34} -4.90237 q^{35} -2.89017 q^{36} +4.91092 q^{37} -2.09641 q^{38} -2.11434 q^{39} -1.00000 q^{40} -10.0332 q^{41} +1.62468 q^{42} +7.00187 q^{43} +1.00000 q^{44} +2.89017 q^{45} -3.56759 q^{46} +9.05617 q^{47} +0.331408 q^{48} +17.0333 q^{49} +1.00000 q^{50} +0.968804 q^{51} -6.37989 q^{52} +10.4014 q^{53} -1.95205 q^{54} -1.00000 q^{55} +4.90237 q^{56} -0.694765 q^{57} -2.29315 q^{58} +13.4141 q^{59} -0.331408 q^{60} -1.92859 q^{61} +6.50101 q^{62} -14.1687 q^{63} +1.00000 q^{64} +6.37989 q^{65} +0.331408 q^{66} +5.86942 q^{67} +2.92330 q^{68} -1.18233 q^{69} -4.90237 q^{70} +14.8467 q^{71} -2.89017 q^{72} +1.00000 q^{73} +4.91092 q^{74} +0.331408 q^{75} -2.09641 q^{76} +4.90237 q^{77} -2.11434 q^{78} -4.63200 q^{79} -1.00000 q^{80} +8.02358 q^{81} -10.0332 q^{82} +5.01023 q^{83} +1.62468 q^{84} -2.92330 q^{85} +7.00187 q^{86} -0.759967 q^{87} +1.00000 q^{88} +4.69580 q^{89} +2.89017 q^{90} -31.2766 q^{91} -3.56759 q^{92} +2.15449 q^{93} +9.05617 q^{94} +2.09641 q^{95} +0.331408 q^{96} +5.24479 q^{97} +17.0333 q^{98} -2.89017 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 14 q^{2} + 6 q^{3} + 14 q^{4} - 14 q^{5} + 6 q^{6} + 4 q^{7} + 14 q^{8} + 24 q^{9}+O(q^{10}) \) 14 * q + 14 * q^2 + 6 * q^3 + 14 * q^4 - 14 * q^5 + 6 * q^6 + 4 * q^7 + 14 * q^8 + 24 * q^9	\( 14 q + 14 q^{2} + 6 q^{3} + 14 q^{4} - 14 q^{5} + 6 q^{6} + 4 q^{7} + 14 q^{8} + 24 q^{9} - 14 q^{10} + 14 q^{11} + 6 q^{12} + 4 q^{13} + 4 q^{14} - 6 q^{15} + 14 q^{16} + 20 q^{17} + 24 q^{18} - 14 q^{20} + 25 q^{21} + 14 q^{22} - 4 q^{23} + 6 q^{24} + 14 q^{25} + 4 q^{26} + 21 q^{27} + 4 q^{28} + 7 q^{29} - 6 q^{30} + 8 q^{31} + 14 q^{32} + 6 q^{33} + 20 q^{34} - 4 q^{35} + 24 q^{36} + 17 q^{37} + 7 q^{39} - 14 q^{40} - 14 q^{41} + 25 q^{42} + 12 q^{43} + 14 q^{44} - 24 q^{45} - 4 q^{46} + 28 q^{47} + 6 q^{48} + 20 q^{49} + 14 q^{50} - 13 q^{51} + 4 q^{52} + 13 q^{53} + 21 q^{54} - 14 q^{55} + 4 q^{56} - 23 q^{57} + 7 q^{58} + 36 q^{59} - 6 q^{60} + 25 q^{61} + 8 q^{62} + 45 q^{63} + 14 q^{64} - 4 q^{65} + 6 q^{66} + 20 q^{68} - 7 q^{69} - 4 q^{70} + 17 q^{71} + 24 q^{72} + 14 q^{73} + 17 q^{74} + 6 q^{75} + 4 q^{77} + 7 q^{78} + 10 q^{79} - 14 q^{80} + 58 q^{81} - 14 q^{82} - 6 q^{83} + 25 q^{84} - 20 q^{85} + 12 q^{86} + 44 q^{87} + 14 q^{88} + 36 q^{89} - 24 q^{90} - 15 q^{91} - 4 q^{92} - 2 q^{93} + 28 q^{94} + 6 q^{96} - 19 q^{97} + 20 q^{98} + 24 q^{99}+O(q^{100}) \) 14 * q + 14 * q^2 + 6 * q^3 + 14 * q^4 - 14 * q^5 + 6 * q^6 + 4 * q^7 + 14 * q^8 + 24 * q^9 - 14 * q^10 + 14 * q^11 + 6 * q^12 + 4 * q^13 + 4 * q^14 - 6 * q^15 + 14 * q^16 + 20 * q^17 + 24 * q^18 - 14 * q^20 + 25 * q^21 + 14 * q^22 - 4 * q^23 + 6 * q^24 + 14 * q^25 + 4 * q^26 + 21 * q^27 + 4 * q^28 + 7 * q^29 - 6 * q^30 + 8 * q^31 + 14 * q^32 + 6 * q^33 + 20 * q^34 - 4 * q^35 + 24 * q^36 + 17 * q^37 + 7 * q^39 - 14 * q^40 - 14 * q^41 + 25 * q^42 + 12 * q^43 + 14 * q^44 - 24 * q^45 - 4 * q^46 + 28 * q^47 + 6 * q^48 + 20 * q^49 + 14 * q^50 - 13 * q^51 + 4 * q^52 + 13 * q^53 + 21 * q^54 - 14 * q^55 + 4 * q^56 - 23 * q^57 + 7 * q^58 + 36 * q^59 - 6 * q^60 + 25 * q^61 + 8 * q^62 + 45 * q^63 + 14 * q^64 - 4 * q^65 + 6 * q^66 + 20 * q^68 - 7 * q^69 - 4 * q^70 + 17 * q^71 + 24 * q^72 + 14 * q^73 + 17 * q^74 + 6 * q^75 + 4 * q^77 + 7 * q^78 + 10 * q^79 - 14 * q^80 + 58 * q^81 - 14 * q^82 - 6 * q^83 + 25 * q^84 - 20 * q^85 + 12 * q^86 + 44 * q^87 + 14 * q^88 + 36 * q^89 - 24 * q^90 - 15 * q^91 - 4 * q^92 - 2 * q^93 + 28 * q^94 + 6 * q^96 - 19 * q^97 + 20 * q^98 + 24 * q^99

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